The present invention relates to facial recognition and the open mouth problem and, more particularly, but not exclusively to a method and apparatus for three dimensional facial recognition that can distinguish between different expressions of the same face on the one hand and different faces on the other hand.
An important question in understanding the structure of facial appearance, is what are the invariants of a human face under various expressions. The change of a face by expressions makes modelling of the face and extraction of features that are not influenced by those changes a challenging task.
It was previously suggested to treat faces as deformable surfaces in the context of Riemannian geometry, and modelling facial expressions as near-isometric transformations of the facial surface. The method of bending-invariant canonical forms was used to construct a representation of the faces, invariant to such isometric transformations. The isometric model, however, has difficulties in handling facial expressions that change the topology of the facial surface. One such example is comparing a face with an open mouth to one with a closed mouth.
That is, how can someone's face be given a unique description, that does not change by his or her expression. Important examples include the problem of face recognition in computer vision, texture mapping for facial animation in computer graphics, emotion interpretation in psychology, and measurement of geometric parameters of the face in cosmetic surgery. The variability of the face appearance due to the non-rigid structure of the human face makes this a non-trivial task and challenges for a convenient model to analyze the nature of facial expressions. In previous work we proposed an isometric model for the face geometry, according to which expressions can be approximated by metric preserving transformations of the facial surface. The use of such a model allows us to use the bending-invariant canonical forms in order to construct an expression-invariant representation of the face. Our isometric model was shown to be applicable to strong facial expressions, but it implicitly assumes that facial expressions are topology-preserving. Thus we had a problem comparing faces with an open mouth to those with a closed one, which is a case in which the topology is not preserved.
FIG. 1A demonstrates this phenomenon by showing the geodesics 3, 4 and 5 between two points on the upper and the lower lips of a face 2. As long as the mouth is closed, the geodesics cross the lips without any significant change, even for extreme facial expressions, compare geodesics 3 and 4. However, opening the mouth changes completely the length of the minimal geodesics. In this case, the geodesic between the two lips passes along the lip contour, as indicated by reference numeral 5. In other words, our previous model always required that in all expressions the mouth has to be either always closed or always open.
There is thus a widely recognized need for, and it would be highly advantageous to have, a facial recognition system devoid of the above limitations, and able to recognize the face irrespective of whether the mouth is open or closed, overcoming the fact that the two cases are topologically different.